JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (12): 23-27.doi: 10.6040/j.issn.1671-9352.0.2014.506

Previous Articles     Next Articles

(λ, μ)-anti-fuzzy rough subgroup

BO Chun-xin, YAO Bing-xue   

  1. School of Mathematics Science, Liaocheng University, Liaocheng 252059, Shandong, China
  • Received:2014-11-12 Revised:2015-04-21 Online:2015-12-20 Published:2015-12-23

Abstract: The definitions of (λ, μ) anti-fuzzy subgroup and (λ, μ) anti-fuzzy normal subgroup were introduced first and their properties were discussed. Then based on the new congruence relation defined from (λ, μ) anti-fuzzy normal subgroup, the concepts of (λ, μ) anti-fuzzy rough subgroup and (λ, μ) anti-fuzzy rough normal subgroup were defined, and some properties were researched.

Key words: (λ, μ) anti-fuzzy rough subgroup, congruence relation, (λ, μ)-anti-fuzzy rough normal subgroup

CLC Number: 

  • O153
[1] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Sciences, 1982, 11(5):341-356.
[2] PAWLAK Z. Rough set: theoretical aspects of reasoning about data[M]. Dordrecht: Kluwer Academic Publishers, 1991.
[3] ZADEH L A. Fuzzy sets[J].Information and Control, 1965, 8:338-351.
[4] ROSENFELD A. Fuzzy groups[J]. J Math Anal Appl, 1971, 35:512-517.
[5] BISWAS R. Fuzzy subgroups and anti-fuzzy subgroups[J]. Fuzzy Sets and Systems, 1990, 35(1):121-125.
[6] 沈正维. 一个群的反模糊子群[J]. 辽宁师范大学学报:自然科学版, 1995, 18(2): 99-101. SHEN Zhengwei. Anti-fuzzy subgroups of a group[J]. Journal of Liaoning Normal University: Natural Science Edition, 1995, 18(2):99-101.
[7] YUAN X, ZHANG C, REN Y. Generalized fuzzy groups and many-valued implications[J]. Fuzzy Sets and Systems, 2003, 138(1): 205-211.
[8] YAO B. (λ, μ)-fuzzy normal subgroups and (λ, μ)-fuzzy quotient subgroups[J]. The Journal of Fuzzy Mathematics, 2005, 13(3):695-705.
[9] 肖丙峰,姚炳学. (λ, μ)-反模糊商群[J].聊城大学学报:自然科学版,2011,2(24):28-30. XIAO Bingfeng, YAO Bingxue. (λ, μ) Anti-fuzzy quotient group[J]. Journal of Liaocheng University: Natural Science Edition, 2011, 2(24):28-30.
[10] KUROKI N, WANG P P. The lower and upper approximations in a fuzzy group[J]. Information Sciences, 1996, 90:203-220.
[11] NANDA S, MAJUMDAR S. Fuzzy rough sets[J]. Fuzzy Sets and Systems, 1992, 45(2):157-160.
[12] 张金玲,张振良.模糊粗糙子群[J].模糊系统与数学,2004,18(4):46-48. ZHANG Jinling, ZHANG Zhenliang. Fuzzy rough subgroups[J]. Fuzzy Systems and Mathematics, 2004, 18(4):46-48.
[13] 郝翠霞,齐玉霞.(λ, μ)-模糊粗糙子群[J].聊城大学学报:自然科学版,2014, 27(3):50-53, 60. HAO Cuixia. QI Yuxia. (λ, μ) -Fuzzy rough subgroups[J]. Journal of Liaocheng University: Natural Science Edition, 2014, 27(3):50-53, 60.
[1] . The number of homomorphisms from metacyclic groups to metacyclic groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 17-22.
[2] WEN Xian-hong, WU Hong-bo*. The prime reverse deductive system of locally finite #br# BL-algebras with properties [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(2): 36-41.
[3] LIU Lu-lu1, FU Wen-qing2, LI Sheng-gang1*. Characterizations of fuzzy subinclines, fuzzy ideals, fuzzy filters and fuzzy congruence relations [J]. J4, 2011, 46(11): 48-52.
[4] LIU Chun-hui1, XU Luo-shan2. On ideals of residuated lattices [J]. J4, 2010, 45(4): 66-71.
[5] QIN Xue-cheng, LIU Chun-hui*. Fuzzy ⊙-ideals in regular residuated lattices [J]. J4, 2010, 45(10): 66-70.
Full text



No Suggested Reading articles found!